Peto's paradox is the observation, named after Richard Peto, that at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism.[1] For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales.[2] This is despite the fact that a whale has many more cells than a human. If the probability of carcinogenesis were constant across cells, one would expect whales to have a higher incidence of cancer than humans.

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Peto, a statistical epidemiologist at the University of Oxford, first formulated the paradox in 1977.[3] Writing an overview of the multistage model of cancer, Peto noted that, on a cell-for-cell basis, humans were much less susceptible to cancer than mice:

A man has 1000 times as many cells as a mouse... and we usually live at least 30 times as long as mice. Exposure of two similar organisms to risk of carcinoma, one for 30 times as long as the other, would give perhaps 304 or 306 (i.e., a million or a billion) times the risk of carcinoma induction per epithelial cell. However, it seems that, in the wild, the probabilities of carcinoma induction in mice and in men are not vastly different. Are our stem cells really, then, a billion or a trillion times more "cancerproof" than murine stem cells? This is biologically pretty implausible; if human DNA is no more resistant to mutagenesis in vitro than mouse DNA, why don't we all die of multiple carcinomas at an early age?

Within members of the same species, cancer risk and body size appear to be positively correlated, even once other risk factors are controlled for.[5] A 25-year longitudinal study of 17,738 male British civil servants, published in 1998, showed a positive correlation between height and cancer incidence with a high degree of statistical confidence, even after risk factors like smoking were controlled for.[6] A similar 2011 study of more than one million British women found strong statistical evidence of a relationship between cancer and height, even after controlling for a number of socioeconomic and behavioral risk factors.[7] A 2011 analysis of the causes of death of 74,556 domesticated North American dogs found that cancer incidence was lowest in the smaller breeds, confirming the results of earlier studies.[8]

Across species, however, the relationship breaks down. A 2015 study, using data from necropsies performed by the San Diego Zoo, surveyed results from 36 different mammalian species, ranging in size from the 51-gram striped grass mouse to the 4,800-kilogram elephant, nearly 100,000 times larger. The study found no relationship between body size and cancer incidence, offering empirical support for Peto's initial observation.[9]

The evolution of multicellularity has required the suppression of cancer to some extent,[10] and connections have been found between the origins of multicellularity and cancer.[11][12] In order to build larger and longer-lived bodies, organisms required greater cancer suppression. Evidence suggests that large organisms such as elephants have more adaptations that allow them to evade cancer.[13] The reason that intermediate-sized organisms have relatively few of these genes may be because the advantage of preventing cancer these genes conferred was, for moderately-sized organisms, outweighed by their disadvantages—particularly reduced fertility.[14]

Various species have evolved different mechanisms for suppressing cancer.[15] A paper in Cell Reports in January 2015 claimed to have found genes in the bowhead whale (Balaena mysticetus) that may be associated with longevity.[16] Around the same time, a second team of researchers identified a polysaccharide in the naked mole-rat that appeared to block the development of tumors.[17] In October 2015, two independent studies showed that elephants have 20 copies of tumor suppressor gene TP53 in their genome, where humans and other mammals have only one.[18] Additional research showed 14 copies of the gene present in the DNA of preserved mammoths, but only one copy of the gene in the DNA of manatees and hyraxes, the elephant's closest living relatives.[19] The results suggest an evolutionary relationship between animal size and tumor suppression, as Peto had theorized.

A 2014 paper in Evolutionary Applications by Maciak and Michalak emphasized what they termed "a largely underappreciated relation of cell size to both metabolism and cell-division rates across species" as key factors underlying the paradox, and concluded that "larger organisms have bigger and slowly dividing cells with lower energy turnover, all significantly reducing the risk of cancer initiation."[20]

Maciak and Michalak argue that cell size is not uniform across mammalian species, making body size an imperfect proxy for the number of cells in an organism. (For example, the volume of an individual red blood cell of an elephant is roughly four times that of one from a common shrew.)[21] Furthermore, larger cells divide more slowly than smaller ones, a difference which compounds exponentially over the life-span of the organism. Fewer cell divisions means fewer opportunities for cancer mutations, and mathematical models of cancer incidence are highly sensitive to cell-division rates.[22] Additionally, larger animals generally have lower basal metabolic rates, following a well-defined inverse logarithmic relationship. Consequently, their cells will incur less damage over time per unit of body mass. Combined, these factors may explain much of the apparent paradox.

It has been suggested that malignant tumors are disadvantaged in larger hosts. In particular, it is hypothesized that natural selection acting on competing phenotypes among the cancer cell population will tend to favor aggressive “cheaters” that then grow as a tumor on their parent tumor, creating a hypertumor that damages or destroys the original neoplasm. In larger organisms, tumors need more time to reach lethal size, so hypertumors have more time to evolve. So, in large organisms, cancer may be more common and less lethal.[23]

The apparent ability of bigger animals to suppress cancer across very large numbers of cells has spurred an active field of medical research.[14] In one experiment, laboratory mice were genetically altered to express active TP53 tumor antigens, similar to the ones found in elephants. The mutated mice exhibited increased tumor suppression ability, but also showed signs of premature aging.[24]

^Kobayashi, H; Man, S (15 April 1993). "Acquired multicellular-mediated resistance to alkylating agents in cancer". Proceedings of the National Academy of Sciences of the United States of America. 90 (8): 3294–8. doi:10.1073/pnas.90.8.3294.